 Example 05.08 Activity Coefficient of the Monomer in a Polymer Using the Athermal

Flory-Huggins Equation

problem:

Calculate the activity coefficient of the monomer in a polymer using the athermal Flory-Huggins equation. For the calculation the following volumes should be used:

v1 = 70 cm3/mol v2 = 70000 cm3/mol

general

constants

and

definitions:  input data  Liquid molar volumes of the components Solution

Using equation 5.33, the activity coefficient can be calculated from the volume fractions q of the components in the mixture: For the activity coefficient, the following expression results: The surface fraction vector is calculated from the mole fraction vector via: Simplification of the expression for the activity coefficient leads to: To avoid the singularity at the pure components, the following function V should be used, which provides identical values without the singularity.   Calculation should be performed for a monomer mole fraction of 0.2:   This results in the following volume fractions: The following values for the activity coefficients can be found:  The same function can now be used to plot the activity coefficients as function of composition:   Or in logarithmic form: Plotting the logarithm of the ratio of the activity coefficients as function of concentration leads to: The curvature above is very typically for strongly assymetric systems with negative deviation from Raoult's Law.